AIC_Ch12 - 12 Introduction to Switched-Capacitor Circuits...

12Introduction to Switched-CapacitorCircuitsOur study of amplifiers in previous chapters has dealt with only cases where the input signal iscontinuously available and applied to the circuit and the output signal is continuously observed.Called “continuous-time” circuits, such amplifiers find wide application in audio, video, and high-speed analog systems. In many situations, however, we may sense the input only at periodic instantsof time, ignoring its value at other times. The circuit then processes each “sample,” producing avalid output at the end of each period. Such circuits are called “discrete-time” or “sampled-data”systems.In this chapter, we study a common class of discrete-time systems called “switched-capacitor(SC) circuits.” Our objective is to provide the foundation for more advanced topics such as filters,comparators, ADCs, and DACs. Most of our study deals with switched-capacitor amplifiers butthe concepts can be applied to other discrete-time circuits as well. Beginning with a general viewof SC circuits, we describe sampling switches and their speed and precision issues.Next, weanalyze switched-capacitor amplifiers, considering unity-gain, noninverting, and multiply-by-twotopologies. Finally, we examine a switched-capacitor integrator.12.1General ConsiderationsIn order to understand the motivation for sampled-data circuits, let us first consider the simplecontinuous-time amplifier shown in Fig.12.1(a).Used extensively with bipolar op amps, thiscircuit presents a difficult issue if implemented in CMOS technology. Recall that, to achieve ahigh voltage gain, the open-loop output resistance of CMOS op amps is maximized, typicallyapproaching hundreds of kilo-ohms. We therefore suspect that2heavily drops the open-loopgain, degrading the precision of the circuit. In fact, with the aid of the simple equivalent circuit395

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Chapter 12. Introduction to Switched-Capacitor Circuits396RR12outVinVRR12outVinVAVRoutXVXv-(a)(b)Figure 12.1.(a) Continuous-time feedback amplifier, (b) equivalent circuit of (a).shown in Fig. 12.1(b), we can write1211212 1and hence212112112 2Equation (12.2) implies that, compared to the case where0, the closed-loop gain suffersfrom inaccuracies in both the numerator and the denominator. Also, the input resistance of theamplifier, approximately equal to1, loads the preceding stage while introducing thermal noise.In the circuit of Fig. 12.1(a), the closed-loop gain is set by the ratio of2and1. In order toavoid reducing the open-loop gain of the op amp, we postulate that the resistors can be replaced bycapacitors [Fig. 12.2(a)]. But, how is the bias voltage at nodeset? We may add a large feedbackoutVinV(a)CC12XoutVinV(a)CC12XRFFigure 12.2.(a) Continuous-time feedback amplifier using capacitors, (b) use of resistor to definebias point.

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